Gmail has keyboard shortcuts for features I've never even heard of but they don't have one for "Print".
This is what happens when you live in a tech bubble instead of the real world. I'm guessing someone decreed that "We [at Google] don't want to make printing easy because blah blah paperless lifestyle."
I googled around and did not find any way to assign a keyboard shortcut to it.
(The print icon is set as 'tabindex=0' which means -- as far as I can tell -- that it is supposed to be the default navigation item when pressing 'tab' but that does not seem to be the case at all. I don't know if there is a way to trigger it by 'tabindex' either… tabindex seems like one of those good ideas that doesn't seem to work as expected, or be well-supported.)
I do have a workaround… but I don't think it's probably one that you want… use Mailplane. Its "Print" function seems to replicate pressing the "Print" icon, and brings up the regular macOS print dialogue window. This should mean that you could control the whole thing via Keyboard Maestro. Depending on how badly you want to do this, it might as least be worth checking out the demo of Mailplane? I've used it for years and consider it to be top-notch, and my favorite way to use Gmail on the Mac.
(Since someone might ask or wonder: Kiwi for Gmail just seems to print the entire browser window, which isn't what anyone wants.)